A few questions really, why do you loose all your armies, surely you should only loose the ones you can't pay for, i.e the most expensive troops first, down to the amount you can afford with the capital that you have, Or if you loose all the armies then you should at least have the all the capital generated that go.

I have also noticed inconsistencies when loosing a normal hex to the enemy, sometimes I loose all of my money and sometimes I don't.

The enemy seem to last much too long when you split their holding, they also seem to produce armies and towers far quicker than their land holdings would dictate.

Yes, you are missing something. Pay attention to the amount of money you collect for each hex that you own sans trees. Then watch and you will see that the AI players always stash some money in their capitol so they do not easily get bankrupted. The way to do this is to smash the hut which destroys the bankroll.

Last is that you must be very careful NOT to go bankrupt yourself. It is intended to work that way. You go bankrupt, you lose it all.

My concern is where the enemy takes a hex (that isn't a capital hex) and I loose some of my money, at other times I keep all my money.

As for the enemy he obviously gets more money at start up, because I've had numerous occasions where the enemy starts with a 3 hex area, doesn't produce a soldier on round 1, then produces a spearman on go two, which then manages to survive though it only now has 4 hexes - shouldn't happpen.

And again I've noticed how the enemy will often hold an area much too small to sustain the troops, and though it can't attack goes on for many turns without dying out. it often takes another hex taken to kill, it's almost as though the program doesn't always update the totals if no action is taken by the AI.

Each contigious hex gets $5 at the start of the game except if it is encumbered with a tree at which point special rules apply depending on where the tree is located with respect to the capitol.

Each contigious hex gets $1 per day played if it is not covered by a tree.

Peons cost $2 per day
Spearmen cost $6 per day
Knights cost $18 per day
Barons cost $54 per day. (rarely do you need a baron except against human players)

The reason you lose money is that you don't have enough territory to support the men on that area. See how much they cost per day above.

Your description of a 3 hex territory making a spearman on day 2 tells me that you did not pay close attention to the moves and $ allocated in the game. This circumstance occurs is when a player joins two territories which combines the money in one capitol, then the territory is cut in two by another player. This can happen as each player moves in turn and if you are not paying very close attention, you will miss it. This can also happen if a territory has more than 3 hexes at startup, but some of those hexes are taken by players in prior moves. Look closely at the $ you have on each 3 hex territory, especially those that have a hex covered by a tree. You will quickly see how this works.

An enemy can survive for many turns with insufficient territory to sustain himself only if he has $ stashed in his capitol.

I've tested this thoroughly. I checked $ in all territories on the island, then I verified that as each player grew, he could only do so in the amount available for play, and I checked that players went bankrupt at the appropriate time. At one time, I found a bug in the way money was handled for territories on the right edge of the island. Sean corrected this a couple of years ago. it no longer happens.

Spend some time playing. Learn to be an effective player. Enjoy the game.